Bivariant (hermitian) K-theory and applications

Abstract: Abstract: Bivariant algebraic K-theory is a functor from a category of associative algebras over a commutative ring to a certain triangulated category; this functor is homotopy invariant, matricially stable and excisive and is universal with those properties. Weibel's homotopy algebraic $K$-theory is recovered as a $\hom$ in the above triangulated category.

In the talk we shall explain how this bivariant theory --and its newly hatched hermitian version-- is used to tackle a long standing problem in the theory of graph algebras, which asserts that for a certain family of these algebras, $K_0$ is a complete invariant of its isomorphism class.

commutative algebraalgebraic geometryalgebraic topologygeometric topologyK-theory and homology

Audience: researchers in the topic

electronic Algebraic K-theory Seminar

Series comments: Description: Research seminar on algebraic K-theory